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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Updated: Feb 16, 2026

Development and Functionalization of Electrolyte-Gated Graphene Field-Effect Transistor for Biomarker Detection
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Two-component structural phase-field crystal models for graphene symmetries.

K L M Elder1, M Seymour2, M Lee2

  • 1Department of Physics, Centre for the Physics of Materials, McGill University, 3600 Rue University, Montreal, Quebec, Canada H3A 2T8 kate.elder@mail.mcgill.ca.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|January 10, 2018
PubMed
Summary

This study models two-component graphene growth, exploring hydrogen's role in grain boundaries and dendritic patterns. The findings offer insights into chemical vapour deposition-grown graphene structures.

Keywords:
dendritic structuresgraphenephase-field crystal modelling

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Surface Science

Background:

  • Chemical vapour deposition (CVD) is crucial for graphene synthesis.
  • Understanding graphene growth mechanisms, particularly grain boundaries and morphologies, is essential.
  • Previous models (Seymour & Provatas 2016, Greenwood et al. 2011) provide frameworks for studying graphene properties.

Purpose of the Study:

  • To extend existing models for two-component graphene.
  • To investigate the influence of hydrogen on graphene grain boundaries and dendritic growth.
  • To compare and contrast the behavior predicted by two distinct modeling approaches.

Main Methods:

  • Adaptation of the three-point XPFC model to two components for CVD graphene.
  • Modification of a two-point XPFC model into a two-component graphene model.
  • Examination of equilibrium properties and comparison of model predictions.

Main Results:

  • The first model elucidates potential roles of hydrogen in graphene grain boundaries.
  • The second model reveals hydrogen's impact on dendritic growth morphologies in graphene.
  • Model predictions for dendritic growth are validated against new experimental data.

Conclusions:

  • The developed two-component models provide valuable tools for studying graphene growth.
  • Hydrogen plays a significant role in shaping graphene's microstructural features.
  • This work bridges atomistic interfaces and macroscopic dendritic patterns in graphene synthesis.